The cat is said to be Elizabeth Montgomery's cat, named Zip Zip. Zip Zip, was also the cat from "The Cat's Meow", when he/she played a stray found on the docks of Chicago, which Darrin first accused of being Samantha in disguise.
Louise is supposed to be pregnant and yet she's not showing and there's no baby. And she's drinking martinis like she was when she "found out".
In this episode, the picture above the Stevens' living room fireplace is a print of "The Old Guitarist" painted by Pablo Picasso during his 'Blue Period' in 1903/1904.